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Collection of discussions regarding volume, vertices, dissection, g-holed tori, and other subjects.
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52B: Polytopes and polyhedra Here are a few files concerning geometric objects made from straight pieces: polygons, polyhedra, and generalizations. History Applications and related fields Questions regarding the underlying spaces (and algebraic invariants) are included on the topology pages. Classic questions regarding polygons and...Comprehensive list of links to sites on geometric properties of the shapes.
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The Geometry Junkyard: Polyhedra and Polytopes This page includes pointers on geometric properties of polygons, polyhedra, and higher dimensional polytopes (particularly convex polytopes Other pages of the junkyard collect related information on triangles, tetrahedra, and simplices, cubes and hypercubes, polyhedral models, and symmetry of regular polytopes....Regular, rectified, and truncated polytopes with normal and hidden-detail-removed projections. Images, animations, and links.
http://home.inreach.com/rtowle/Polytopes/polytope.html
Definitions, pictures, templates, and coordinates of the regular 3d and 4d polytopes. Also includes waterman polyhedra, polar and star spheres, and the time star.
http://astronomy.swin.edu.au/~pbourke/polyhedra/
Polytopes and optimal packing of p points in n dimensional spheres. Contains a java applet based on a model which allows for generation of multidimensional regular and semi-regular polytopes.
http://presh.com/hovinga
Enumeration, cartesian coordinates of vertices, naming, and counting the shapes.
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Polyhedron, Polyhedra, Polytopes Numericana This set of articles started with a simple question (below) about hexahedra, which may still be found [in abbreviated form] at its original location in our main Geometry Page Hexahedra. The cube is not the only polyhedron with 6 faces....Vertex figures, filling, faceting diagrams, stellation, defining polytopes through generators, trimethoric and trisynaptic polyhedra, space-filling polyhedra, lost stellations of the icosahedron, and links.
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Polyhedra Index Page General theory of polytopes and polyhedra Stellation and facetting Space-filling polyhedra Other resources What's new 21 May 2005. Icosahedral precursors Renamed yet again from Icosahedral templates to reflect another change in terminology. Some useful clarifications, including a slight reordering of...Derivation of volume equations for regular polygons, polyhedra, and polytopes, with images.
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Regular Polygons Contains implementations of many of the formulas derived below. Regular polygons Mathematica notebook Regular Polygons Project Regular Polyhedra Regular Polytopes I. Geometric Properties Below is a table and diagram summarizing the variables used in the explanation. Angles are measured in...Educational toys used to teach geometry and model building to create squares, spheres, stars and other regular shapes with sticks and connecting pieces. Products include kits and lesson plans.
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Zome Educators Zome is based on a version of the 61-zone structural system which includes purely mathematical models from tilings to hyperspace projections, as well as molecular models of quasicrystals and fullerenes, and architectural space frame structures. Zome's balls (nodes) and struts...Three-dimensional objects constructed by slotting together a series of planar cross sections made from card. Downloadable templates in PDF, PS and Word formats.
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Maths Year 2000 Sliceforms book and poster Section 2How to make and assemble the models Section 3 Sliceform templates and download instructions Adobe Acrobat Word 6 EMF and EPS files Section 4 Sliceform Gallery A Sliceform tetrahedron A Sliceform zonohedron A Sliceform hyperbolic...Describes a theorem for finding an area of simple lattice polygons. Includes proof and Java applet simulation.
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Pick's Theorem: An Interactive Activity An interactive column using Java applets by Alex Bogomolny Pick's Theorem May 1998 Georg Alexander Pick, born in 1859 in Vienna, perished around 1943 in the Theresienstadt concentration camp 9] First published in 1899, the theorem was brought to broad...